In the case \(d=g\)  and \(n=0\) , the tropical shadow of these constructions has been discovered independently in [1]} under the name break divisor. An admissible divisor \(D\)  on a quasi-stable graph \(G\)  of type \((g,0)\)  is said to be a break divisor, if there is a spanning tree \(T\)  of \(G\)  as well as a map \(\phi \colon E(G)-E(T)\rightarrow V(G)\)  such that \(\phi (e)\)  is adjacent to \(e\)  and
\(D=\sum _{v\in V(G)}h(v)+\sum _{e\in E(G)-E(T)}\phi (e) \ .\) 
